MinT - Best Known (78, 78+72, s)-Nets in Base 9

Best Known (78, 78+72, s)-Nets in Base 9

(78, 78+72, 232)-Net over F₉ — Constructive and digital

Digital (78, 150, 232)-net over F₉, using

t-expansion [i] based on digital (77, 150, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 75, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(78, 78+72, 330)-Net over F₉ — Digital

Digital (78, 150, 330)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+72, 16869)-Net in Base 9 — Upper bound on s

There is no (78, 150, 16870)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137156 121268 726599 465592 350390 817030 268190 774669 609571 551356 990237 289782 578737 167838 186744 576205 590767 744359 564236 094910 205543 671425 686738 941505 > 9¹⁵⁰ [i]