MinT - Best Known (116, 116+117, s)-Nets in Base 4

Best Known (116, 116+117, s)-Nets in Base 4

(116, 116+117, 130)-Net over F₄ — Constructive and digital

Digital (116, 233, 130)-net over F₄, using

t-expansion [i] based on digital (105, 233, 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+117, 168)-Net over F₄ — Digital

Digital (116, 233, 168)-net over F₄, using

t-expansion [i] based on digital (115, 233, 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+117, 1868)-Net in Base 4 — Upper bound on s

There is no (116, 233, 1869)-net in base 4, because

1 times m-reduction [i] would yield (116, 232, 1869)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 48 510330 092004 696336 661057 826529 257619 564937 665681 628751 302622 031227 841180 285101 012408 184788 627733 731953 941225 298357 745304 049547 825626 218376 > 4²³² [i]