MinT - Best Known (114−35, 114, s)-Nets in Base 4

Best Known (114−35, 114, s)-Nets in Base 4

(114−35, 114, 312)-Net over F₄ — Constructive and digital

Digital (79, 114, 312)-net over F₄, using

trace code for nets [i] based on digital (3, 38, 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]

(114−35, 114, 483)-Net over F₄ — Digital

Digital (79, 114, 483)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−35, 114, 24016)-Net in Base 4 — Upper bound on s

There is no (79, 114, 24017)-net in base 4, because

1 times m-reduction [i] would yield (79, 113, 24017)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 107 897359 704254 253327 852657 742935 807121 683167 141224 144211 335620 960340 > 4¹¹³ [i]