MinT - Best Known (154−103, 154, s)-Nets in Base 8

Best Known (154−103, 154, s)-Nets in Base 8

(154−103, 154, 98)-Net over F₈ — Constructive and digital

Digital (51, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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]

(154−103, 154, 144)-Net over F₈ — Digital

Digital (51, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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]

(154−103, 154, 1420)-Net in Base 8 — Upper bound on s

There is no (51, 154, 1421)-net in base 8, because

1 times m-reduction [i] would yield (51, 153, 1421)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 534501 483533 324979 130953 346316 029900 973140 597047 458602 325956 480105 521782 122423 433163 866792 676164 245271 502411 855267 851592 096149 857742 079008 > 8¹⁵³ [i]