MinT - Best Known (110−31, 110, s)-Nets in Base 4

Best Known (110−31, 110, s)-Nets in Base 4

(110−31, 110, 384)-Net over F₄ — Constructive and digital

Digital (79, 110, 384)-net over F₄, using

1 times m-reduction [i] based on digital (79, 111, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 37, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(110−31, 110, 662)-Net over F₄ — Digital

Digital (79, 110, 662)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(110−31, 110, 50758)-Net in Base 4 — Upper bound on s

There is no (79, 110, 50759)-net in base 4, because

1 times m-reduction [i] would yield (79, 109, 50759)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 421264 468642 593814 471884 237127 399632 844297 751917 208846 776872 924448 > 4¹⁰⁹ [i]