MinT - Best Known (85, 156, s)-Nets in Base 4

Best Known (85, 156, s)-Nets in Base 4

(85, 156, 130)-Net over F₄ — Constructive and digital

Digital (85, 156, 130)-net over F₄, using

2 times m-reduction [i] based on digital (85, 158, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 79, 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]

(85, 156, 156)-Net over F₄ — Digital

Digital (85, 156, 156)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(85, 156, 2121)-Net in Base 4 — Upper bound on s

There is no (85, 156, 2122)-net in base 4, because

1 times m-reduction [i] would yield (85, 155, 2122)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2108 824682 389289 446433 575996 979881 115751 192168 056737 510805 016150 719843 488038 386480 357747 131816 > 4¹⁵⁵ [i]