MinT - Best Known (179−81, 179, s)-Nets in Base 4

Best Known (179−81, 179, s)-Nets in Base 4

(179−81, 179, 130)-Net over F₄ — Constructive and digital

Digital (98, 179, 130)-net over F₄, using

5 times m-reduction [i] based on digital (98, 184, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 92, 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]

(179−81, 179, 179)-Net over F₄ — Digital

Digital (98, 179, 179)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(179−81, 179, 2478)-Net in Base 4 — Upper bound on s

There is no (98, 179, 2479)-net in base 4, because

1 times m-reduction [i] would yield (98, 178, 2479)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 148493 612541 372877 358688 472961 063413 594516 608608 876171 544496 553752 252904 583139 186444 390513 956194 068401 013759 > 4¹⁷⁸ [i]