MinT - Best Known (100, 100+78, s)-Nets in Base 4

Best Known (100, 100+78, s)-Nets in Base 4

(100, 100+78, 130)-Net over F₄ — Constructive and digital

Digital (100, 178, 130)-net over F₄, using

10 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]

(100, 100+78, 197)-Net over F₄ — Digital

Digital (100, 178, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+78, 2840)-Net in Base 4 — Upper bound on s

There is no (100, 178, 2841)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 148741 530600 634015 509883 861185 430958 693630 573423 943833 769979 297931 798021 047087 875061 353030 330691 035411 561280 > 4¹⁷⁸ [i]