MinT - Best Known (193−118, 193, s)-Nets in Base 4

Best Known (193−118, 193, s)-Nets in Base 4

(193−118, 193, 104)-Net over F₄ — Constructive and digital

Digital (75, 193, 104)-net over F₄, using

t-expansion [i] based on digital (73, 193, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(193−118, 193, 112)-Net over F₄ — Digital

Digital (75, 193, 112)-net over F₄, using

t-expansion [i] based on digital (73, 193, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(193−118, 193, 661)-Net in Base 4 — Upper bound on s

There is no (75, 193, 662)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 162 923855 214176 788361 929274 333179 961494 356811 192242 320735 246295 492615 456331 657452 793550 542472 226409 863399 972519 928480 > 4¹⁹³ [i]