MinT - Best Known (116, 116+139, s)-Nets in Base 4

Best Known (116, 116+139, s)-Nets in Base 4

(116, 116+139, 130)-Net over F₄ — Constructive and digital

Digital (116, 255, 130)-net over F₄, using

t-expansion [i] based on digital (105, 255, 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]

(116, 116+139, 168)-Net over F₄ — Digital

Digital (116, 255, 168)-net over F₄, using

t-expansion [i] based on digital (115, 255, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(116, 116+139, 1398)-Net in Base 4 — Upper bound on s

There is no (116, 255, 1399)-net in base 4, because

1 times m-reduction [i] would yield (116, 254, 1399)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 849 182074 394588 827957 945292 304227 872947 712401 998870 192040 611083 048274 918462 686482 557685 802544 724534 512322 623615 551204 083257 117378 286436 726363 155230 712154 > 4²⁵⁴ [i]