MinT - Best Known (108, 108+139, s)-Nets in Base 4

Best Known (108, 108+139, s)-Nets in Base 4

(108, 108+139, 130)-Net over F₄ — Constructive and digital

Digital (108, 247, 130)-net over F₄, using

t-expansion [i] based on digital (105, 247, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(108, 108+139, 144)-Net over F₄ — Digital

Digital (108, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(108, 108+139, 1182)-Net in Base 4 — Upper bound on s

There is no (108, 247, 1183)-net in base 4, because

1 times m-reduction [i] would yield (108, 246, 1183)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12898 126374 534979 870242 139540 415859 706886 546591 569782 403115 644106 850066 837055 322001 320983 730054 638831 091640 562976 317782 611429 041338 248738 429715 167644 > 4²⁴⁶ [i]