MinT - Best Known (142−46, 142, s)-Nets in Base 4

Best Known (142−46, 142, s)-Nets in Base 4

(142−46, 142, 240)-Net over F₄ — Constructive and digital

Digital (96, 142, 240)-net over F₄, using

4¹ times duplication [i] based on digital (95, 141, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 47, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(142−46, 142, 459)-Net over F₄ — Digital

Digital (96, 142, 459)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−46, 142, 16364)-Net in Base 4 — Upper bound on s

There is no (96, 142, 16365)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 098884 376312 541471 633328 871842 980337 711253 337528 540133 146555 127638 419561 565559 682736 > 4¹⁴² [i]