MinT - Best Known (117, 117+119, s)-Nets in Base 4

Best Known (117, 117+119, s)-Nets in Base 4

(117, 117+119, 130)-Net over F₄ — Constructive and digital

Digital (117, 236, 130)-net over F₄, using

t-expansion [i] based on digital (105, 236, 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]

(117, 117+119, 168)-Net over F₄ — Digital

Digital (117, 236, 168)-net over F₄, using

t-expansion [i] based on digital (115, 236, 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]

(117, 117+119, 1853)-Net in Base 4 — Upper bound on s

There is no (117, 236, 1854)-net in base 4, because

1 times m-reduction [i] would yield (117, 235, 1854)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3049 345768 517828 470045 648911 615333 362166 693607 351901 823557 253962 273042 266918 619188 085237 879528 730540 040459 396387 183469 952915 757504 729563 375466 > 4²³⁵ [i]