MinT - Best Known (90, 90+71, s)-Nets in Base 4

Best Known (90, 90+71, s)-Nets in Base 4

(90, 90+71, 130)-Net over F₄ — Constructive and digital

Digital (90, 161, 130)-net over F₄, using

7 times m-reduction [i] based on digital (90, 168, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 84, 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]

(90, 90+71, 177)-Net over F₄ — Digital

Digital (90, 161, 177)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+71, 2592)-Net in Base 4 — Upper bound on s

There is no (90, 161, 2593)-net in base 4, because

1 times m-reduction [i] would yield (90, 160, 2593)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 160375 152517 749170 787995 720611 118693 272716 577733 571562 353709 235862 669307 945545 672088 319141 633600 > 4¹⁶⁰ [i]