MinT - Best Known (143−59, 143, s)-Nets in Base 4

Best Known (143−59, 143, s)-Nets in Base 4

(143−59, 143, 130)-Net over F₄ — Constructive and digital

Digital (84, 143, 130)-net over F₄, using

13 times m-reduction [i] based on digital (84, 156, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 78, 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]

(143−59, 143, 198)-Net over F₄ — Digital

Digital (84, 143, 198)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(143−59, 143, 3427)-Net in Base 4 — Upper bound on s

There is no (84, 143, 3428)-net in base 4, because

1 times m-reduction [i] would yield (84, 142, 3428)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 087603 215010 826221 691370 917768 711507 597439 777087 180443 365224 683648 976878 725241 283640 > 4¹⁴² [i]