MinT - Best Known (173−75, 173, s)-Nets in Base 4

Best Known (173−75, 173, s)-Nets in Base 4

(173−75, 173, 130)-Net over F₄ — Constructive and digital

Digital (98, 173, 130)-net over F₄, using

11 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]

(173−75, 173, 199)-Net over F₄ — Digital

Digital (98, 173, 199)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−75, 173, 3042)-Net in Base 4 — Upper bound on s

There is no (98, 173, 3043)-net in base 4, because

1 times m-reduction [i] would yield (98, 172, 3043)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 35 950901 881653 307262 819714 615206 160761 338791 418804 180193 801660 505980 440296 284688 505160 903315 851973 731040 > 4¹⁷² [i]