MinT - Best Known (158−73, 158, s)-Nets in Base 4

Best Known (158−73, 158, s)-Nets in Base 4

(158−73, 158, 130)-Net over F₄ — Constructive and digital

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]

(158−73, 158, 150)-Net over F₄ — Digital

Digital (85, 158, 150)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−73, 158, 1980)-Net in Base 4 — Upper bound on s

There is no (85, 158, 1981)-net in base 4, because

1 times m-reduction [i] would yield (85, 157, 1981)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33380 663124 354969 318519 660045 018382 530742 202383 053786 026279 758708 788476 002323 155979 160584 131485 > 4¹⁵⁷ [i]