MinT - Best Known (135, 135+119, s)-Nets in Base 4

Best Known (135, 135+119, s)-Nets in Base 4

(135, 135+119, 130)-Net over F₄ — Constructive and digital

Digital (135, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(135, 135+119, 218)-Net over F₄ — Digital

Digital (135, 254, 218)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(135, 135+119, 2855)-Net in Base 4 — Upper bound on s

There is no (135, 254, 2856)-net in base 4, because

1 times m-reduction [i] would yield (135, 253, 2856)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212 856393 136765 613938 055752 077133 050991 972613 172593 714305 323593 447597 225141 176597 040808 124238 481240 890827 293361 115084 261956 262454 303816 494504 250662 895712 > 4²⁵³ [i]