MinT - Best Known (129−37, 129, s)-Nets in Base 4

Best Known (129−37, 129, s)-Nets in Base 4

(129−37, 129, 384)-Net over F₄ — Constructive and digital

Digital (92, 129, 384)-net over F₄, using

t-expansion [i] based on digital (91, 129, 384)-net over F₄, using
- trace code for nets [i] based on digital (5, 43, 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]

(129−37, 129, 702)-Net over F₄ — Digital

Digital (92, 129, 702)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−37, 129, 48105)-Net in Base 4 — Upper bound on s

There is no (92, 129, 48106)-net in base 4, because

1 times m-reduction [i] would yield (92, 128, 48106)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 115820 024504 245147 408672 372245 622244 035595 294664 449409 803078 946037 803774 663832 > 4¹²⁸ [i]