MinT - Best Known (70, 70+103, s)-Nets in Base 8

Best Known (70, 70+103, s)-Nets in Base 8

(70, 70+103, 98)-Net over F₈ — Constructive and digital

Digital (70, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(70, 70+103, 144)-Net over F₈ — Digital

Digital (70, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(70, 70+103, 150)-Net in Base 8

(70, 173, 150)-net in base 8, using

8¹ times duplication [i] based on (69, 172, 150)-net in base 8, using
- base change [i] based on digital (26, 129, 150)-net over F₁₆, using
  - net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
      - a curve from the manYPoints database [i]

(70, 70+103, 3118)-Net in Base 8 — Upper bound on s

There is no (70, 173, 3119)-net in base 8, because

1 times m-reduction [i] would yield (70, 172, 3119)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 214550 203762 244103 555369 523431 129757 142815 359706 398410 281615 467534 839538 215724 267462 999216 505661 379946 418456 167631 639198 642395 887883 569724 707246 723610 485504 > 8¹⁷² [i]