MinT - Best Known (71, 71+102, s)-Nets in Base 8

Best Known (71, 71+102, s)-Nets in Base 8

(71, 71+102, 98)-Net over F₈ — Constructive and digital

Digital (71, 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]

(71, 71+102, 144)-Net over F₈ — Digital

Digital (71, 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]

(71, 71+102, 156)-Net in Base 8

(71, 173, 156)-net in base 8, using

8¹ times duplication [i] based on (70, 172, 156)-net in base 8, using
- base change [i] based on digital (27, 129, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(71, 71+102, 3250)-Net in Base 8 — Upper bound on s

There is no (71, 173, 3251)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 739602 071503 897005 366906 106783 006598 712129 002162 879080 476800 319800 668402 896802 572437 249331 616514 099172 982106 137581 142860 191313 419120 179342 333157 475745 759992 > 8¹⁷³ [i]