MinT - Best Known (99−44, 99, s)-Nets in Base 4

Best Known (99−44, 99, s)-Nets in Base 4

(99−44, 99, 98)-Net over F₄ — Constructive and digital

Digital (55, 99, 98)-net over F₄, using

1 times m-reduction [i] based on digital (55, 100, 98)-net over F₄, using
- trace code for nets [i] based on digital (5, 50, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(99−44, 99, 115)-Net over F₄ — Digital

Digital (55, 99, 115)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−44, 99, 1527)-Net in Base 4 — Upper bound on s

There is no (55, 99, 1528)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 404568 087736 924064 819936 742237 027877 489913 937696 891394 287613 > 4⁹⁹ [i]