MinT - Best Known (236−157, 236, s)-Nets in Base 4

Best Known (236−157, 236, s)-Nets in Base 4

(236−157, 236, 104)-Net over F₄ — Constructive and digital

Digital (79, 236, 104)-net over F₄, using

t-expansion [i] based on digital (73, 236, 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]

(236−157, 236, 112)-Net over F₄ — Digital

Digital (79, 236, 112)-net over F₄, using

t-expansion [i] based on digital (73, 236, 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]

(236−157, 236, 586)-Net in Base 4 — Upper bound on s

There is no (79, 236, 587)-net in base 4, because

1 times m-reduction [i] would yield (79, 235, 587)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3355 101644 155514 519208 780303 815626 839187 904445 399273 582056 927624 795300 602330 902294 085970 471197 470457 182494 118582 120338 458274 078065 195707 849856 > 4²³⁵ [i]