MinT - Best Known (98−74, 98, s)-Nets in Base 9

Best Known (98−74, 98, s)-Nets in Base 9

(98−74, 98, 78)-Net over F₉ — Constructive and digital

Digital (24, 98, 78)-net over F₉, using

t-expansion [i] based on digital (22, 98, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(98−74, 98, 92)-Net over F₉ — Digital

Digital (24, 98, 92)-net over F₉, using

t-expansion [i] based on digital (23, 98, 92)-net over F₉, using
- net from sequence [i] based on digital (23, 91)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
    - Drinfeld modules of rank 1 [i]

(98−74, 98, 594)-Net in Base 9 — Upper bound on s

There is no (24, 98, 595)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3358 559132 431960 402570 214150 336888 026759 299118 218198 383663 456007 170806 865260 510040 287109 516025 > 9⁹⁸ [i]