MinT - Best Known (96, 96+45, s)-Nets in Base 4

Best Known (96, 96+45, s)-Nets in Base 4

(96, 96+45, 240)-Net over F₄ — Constructive and digital

Digital (96, 141, 240)-net over F₄, using

t-expansion [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]

(96, 96+45, 484)-Net over F₄ — Digital

Digital (96, 141, 484)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(96, 96+45, 20447)-Net in Base 4 — Upper bound on s

There is no (96, 141, 20448)-net in base 4, because

1 times m-reduction [i] would yield (96, 140, 20448)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 943326 348151 358632 277415 831084 473151 216952 748734 230265 523606 906623 365444 324699 195303 > 4¹⁴⁰ [i]