MinT - Best Known (91, 91+39, s)-Nets in Base 4

Best Known (91, 91+39, s)-Nets in Base 4

(91, 91+39, 312)-Net over F₄ — Constructive and digital

Digital (91, 130, 312)-net over F₄, using

2 times m-reduction [i] based on digital (91, 132, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 44, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(91, 91+39, 587)-Net over F₄ — Digital

Digital (91, 130, 587)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+39, 32326)-Net in Base 4 — Upper bound on s

There is no (91, 130, 32327)-net in base 4, because

1 times m-reduction [i] would yield (91, 129, 32327)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 463301 950223 808443 660988 001156 326211 935092 000227 500315 676455 548762 429832 171136 > 4¹²⁹ [i]