MinT - Best Known (179−75, 179, s)-Nets in Base 4

Best Known (179−75, 179, s)-Nets in Base 4

(179−75, 179, 130)-Net over F₄ — Constructive and digital

Digital (104, 179, 130)-net over F₄, using

17 times m-reduction [i] based on digital (104, 196, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 98, 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]

(179−75, 179, 228)-Net over F₄ — Digital

Digital (104, 179, 228)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−75, 179, 3817)-Net in Base 4 — Upper bound on s

There is no (104, 179, 3818)-net in base 4, because

1 times m-reduction [i] would yield (104, 178, 3818)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 147726 152793 159701 639182 044028 327516 901296 435142 307737 549210 038496 620703 350236 223339 237772 595705 782885 002990 > 4¹⁷⁸ [i]