MinT - Best Known (91−27, 91, s)-Nets in Base 4

Best Known (91−27, 91, s)-Nets in Base 4

(91−27, 91, 312)-Net over F₄ — Constructive and digital

Digital (64, 91, 312)-net over F₄, using

4¹ times duplication [i] based on digital (63, 90, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 30, 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]

(91−27, 91, 463)-Net over F₄ — Digital

Digital (64, 91, 463)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(91−27, 91, 27811)-Net in Base 4 — Upper bound on s

There is no (64, 91, 27812)-net in base 4, because

1 times m-reduction [i] would yield (64, 90, 27812)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 532540 056384 959327 009395 976994 554522 088755 997090 632664 > 4⁹⁰ [i]