MinT - Best Known (193−60, 193, s)-Nets in Base 4

Best Known (193−60, 193, s)-Nets in Base 4

(193−60, 193, 312)-Net over F₄ — Constructive and digital

Digital (133, 193, 312)-net over F₄, using

2 times m-reduction [i] based on digital (133, 195, 312)-net over F₄, using
- trace code for nets [i] based on digital (3, 65, 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]

(193−60, 193, 697)-Net over F₄ — Digital

Digital (133, 193, 697)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−60, 193, 29961)-Net in Base 4 — Upper bound on s

There is no (133, 193, 29962)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 157 669456 499251 851762 869150 747497 011476 721804 054956 104210 572975 522291 496698 862732 163742 833302 681717 726761 314312 145280 > 4¹⁹³ [i]