MinT - Best Known (91, 91+69, s)-Nets in Base 4

Best Known (91, 91+69, s)-Nets in Base 4

(91, 91+69, 130)-Net over F₄ — Constructive and digital

Digital (91, 160, 130)-net over F₄, using

10 times m-reduction [i] based on digital (91, 170, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 85, 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]

(91, 91+69, 189)-Net over F₄ — Digital

Digital (91, 160, 189)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+69, 2922)-Net in Base 4 — Upper bound on s

There is no (91, 160, 2923)-net in base 4, because

1 times m-reduction [i] would yield (91, 159, 2923)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 536506 849627 258231 448110 581344 762069 620580 813136 243684 413032 308502 398020 104851 636494 135397 817927 > 4¹⁵⁹ [i]