MinT - Best Known (116, 116+107, s)-Nets in Base 4

Best Known (116, 116+107, s)-Nets in Base 4

(116, 116+107, 130)-Net over F₄ — Constructive and digital

Digital (116, 223, 130)-net over F₄, using

t-expansion [i] based on digital (105, 223, 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+107, 180)-Net over F₄ — Digital

Digital (116, 223, 180)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(116, 116+107, 2239)-Net in Base 4 — Upper bound on s

There is no (116, 223, 2240)-net in base 4, because

1 times m-reduction [i] would yield (116, 222, 2240)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 798241 457272 971860 543088 372971 633832 264854 406991 790106 437206 302348 817492 389225 427075 669883 215969 158081 879629 991260 959023 975790 102051 > 4²²² [i]