MinT - Best Known (115−33, 115, s)-Nets in Base 4

Best Known (115−33, 115, s)-Nets in Base 4

(115−33, 115, 384)-Net over F₄ — Constructive and digital

Digital (82, 115, 384)-net over F₄, using

4¹ times duplication [i] based on digital (81, 114, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 38, 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]

(115−33, 115, 637)-Net over F₄ — Digital

Digital (82, 115, 637)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−33, 115, 44153)-Net in Base 4 — Upper bound on s

There is no (82, 115, 44154)-net in base 4, because

1 times m-reduction [i] would yield (82, 114, 44154)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 431 380443 190862 081368 528617 933434 728702 239374 241006 264863 348831 138557 > 4¹¹⁴ [i]