MinT - Best Known (99, 99+44, s)-Nets in Base 9

Best Known (99, 99+44, s)-Nets in Base 9

(99, 99+44, 756)-Net over F₉ — Constructive and digital

Digital (99, 143, 756)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (1, 23, 16)-net over F₉, using
  - net from sequence [i] based on digital (1, 15)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 1 and N(F) ≥ 16, using
      - a function field by GarcÃa and Quoos [i]
2. digital (76, 120, 740)-net over F₉, using
  - trace code for nets [i] based on digital (16, 60, 370)-net over F₈₁, using
    - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
        a function field by GarcÃa and Quoos [i]

(99, 99+44, 3168)-Net over F₉ — Digital

Digital (99, 143, 3168)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+44, 1804413)-Net in Base 9 — Upper bound on s

There is no (99, 143, 1804414)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28620 645007 559347 969166 364932 541645 044793 140809 889207 853379 969597 641783 608397 877250 229471 524722 334241 751687 155823 674598 193678 423014 228065 > 9¹⁴³ [i]