MinT - Best Known (177−77, 177, s)-Nets in Base 4

Best Known (177−77, 177, s)-Nets in Base 4

(177−77, 177, 130)-Net over F₄ — Constructive and digital

Digital (100, 177, 130)-net over F₄, using

11 times m-reduction [i] based on digital (100, 188, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 94, 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]

(177−77, 177, 201)-Net over F₄ — Digital

Digital (100, 177, 201)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(177−77, 177, 3046)-Net in Base 4 — Upper bound on s

There is no (100, 177, 3047)-net in base 4, because

1 times m-reduction [i] would yield (100, 176, 3047)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9258 544730 298348 577575 266682 159066 280485 673960 588222 762816 337924 429512 998608 592151 726257 211529 456918 293531 > 4¹⁷⁶ [i]