MinT - Best Known (158−63, 158, s)-Nets in Base 4

Best Known (158−63, 158, s)-Nets in Base 4

(158−63, 158, 130)-Net over F₄ — Constructive and digital

Digital (95, 158, 130)-net over F₄, using

20 times m-reduction [i] based on digital (95, 178, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 89, 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]

(158−63, 158, 241)-Net over F₄ — Digital

Digital (95, 158, 241)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−63, 158, 4609)-Net in Base 4 — Upper bound on s

There is no (95, 158, 4610)-net in base 4, because

1 times m-reduction [i] would yield (95, 157, 4610)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 33426 668458 191067 634464 706480 057164 130306 105174 645035 836865 016106 748521 439353 491647 971127 474432 > 4¹⁵⁷ [i]