MinT - Best Known (114−52, 114, s)-Nets in Base 4

Best Known (114−52, 114, s)-Nets in Base 4

(114−52, 114, 98)-Net over F₄ — Constructive and digital

Digital (62, 114, 98)-net over F₄, using

trace code for nets [i] based on digital (5, 57, 49)-net over F₁₆, using
- net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
    - a function field by SÃ©mirat [i]

(114−52, 114, 119)-Net over F₄ — Digital

Digital (62, 114, 119)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−52, 114, 1513)-Net in Base 4 — Upper bound on s

There is no (62, 114, 1514)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 435 267711 914861 698527 835877 264821 764543 777187 448853 969018 532808 010592 > 4¹¹⁴ [i]