MinT - Best Known (100, 100+138, s)-Nets in Base 4

Best Known (100, 100+138, s)-Nets in Base 4

(100, 100+138, 104)-Net over F₄ — Constructive and digital

Digital (100, 238, 104)-net over F₄, using

t-expansion [i] based on digital (73, 238, 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]

(100, 100+138, 144)-Net over F₄ — Digital

Digital (100, 238, 144)-net over F₄, using

t-expansion [i] based on digital (91, 238, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(100, 100+138, 999)-Net in Base 4 — Upper bound on s

There is no (100, 238, 1000)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 207411 555517 826707 422833 467947 583158 736421 421911 561122 341619 309505 361763 434791 892042 748295 137923 646015 164881 174563 147561 606830 497721 083679 386671 > 4²³⁸ [i]