MinT - Best Known (101, 101+117, s)-Nets in Base 4

Best Known (101, 101+117, s)-Nets in Base 4

(101, 101+117, 104)-Net over F₄ — Constructive and digital

Digital (101, 218, 104)-net over F₄, using

t-expansion [i] based on digital (73, 218, 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]

(101, 101+117, 144)-Net over F₄ — Digital

Digital (101, 218, 144)-net over F₄, using

t-expansion [i] based on digital (91, 218, 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]

(101, 101+117, 1291)-Net in Base 4 — Upper bound on s

There is no (101, 218, 1292)-net in base 4, because

1 times m-reduction [i] would yield (101, 217, 1292)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45577 908954 574387 093956 715992 378248 464110 304212 681519 664303 122614 811028 848530 437152 498703 559162 507297 134045 263324 620772 280921 805200 > 4²¹⁷ [i]