MinT - Best Known (142−57, 142, s)-Nets in Base 4

Best Known (142−57, 142, s)-Nets in Base 4

(142−57, 142, 130)-Net over F₄ — Constructive and digital

Digital (85, 142, 130)-net over F₄, using

16 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 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]

(142−57, 142, 216)-Net over F₄ — Digital

Digital (85, 142, 216)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−57, 142, 4029)-Net in Base 4 — Upper bound on s

There is no (85, 142, 4030)-net in base 4, because

1 times m-reduction [i] would yield (85, 141, 4030)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 804607 426389 609921 517571 990456 630127 959963 433854 584077 019760 793370 845383 840233 066287 > 4¹⁴¹ [i]