MinT - Best Known (142−44, 142, s)-Nets in Base 4

Best Known (142−44, 142, s)-Nets in Base 4

(142−44, 142, 312)-Net over F₄ — Constructive and digital

Digital (98, 142, 312)-net over F₄, using

4¹ times duplication [i] based on digital (97, 141, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 47, 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]

(142−44, 142, 549)-Net over F₄ — Digital

Digital (98, 142, 549)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−44, 142, 23196)-Net in Base 4 — Upper bound on s

There is no (98, 142, 23197)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 31 098638 570527 378165 918258 152565 532780 760529 238690 221699 746666 172158 226617 225966 818260 > 4¹⁴² [i]