MinT - Best Known (232−75, 232, s)-Nets in Base 4

Best Known (232−75, 232, s)-Nets in Base 4

(232−75, 232, 450)-Net over F₄ — Constructive and digital

Digital (157, 232, 450)-net over F₄, using

2 times m-reduction [i] based on digital (157, 234, 450)-net over F₄, using
- trace code for nets [i] based on digital (40, 117, 225)-net over F₁₆, using
  - net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
      - a function field by GarcÃa and Quoos [i]

(232−75, 232, 702)-Net over F₄ — Digital

Digital (157, 232, 702)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−75, 232, 27998)-Net in Base 4 — Upper bound on s

There is no (157, 232, 27999)-net in base 4, because

1 times m-reduction [i] would yield (157, 231, 27999)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 923802 252805 631465 716076 090749 981318 440343 398878 213908 904685 875790 413549 943581 541138 895213 176409 856691 983363 722150 055628 034453 256180 117540 > 4²³¹ [i]