MinT - Best Known (154−59, 154, s)-Nets in Base 4

Best Known (154−59, 154, s)-Nets in Base 4

(154−59, 154, 130)-Net over F₄ — Constructive and digital

Digital (95, 154, 130)-net over F₄, using

24 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(154−59, 154, 271)-Net over F₄ — Digital

Digital (95, 154, 271)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−59, 154, 5816)-Net in Base 4 — Upper bound on s

There is no (95, 154, 5817)-net in base 4, because

1 times m-reduction [i] would yield (95, 153, 5817)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 131 011196 239211 344432 863627 957884 655523 362547 974756 111809 834650 335185 483386 586399 198552 872000 > 4¹⁵³ [i]