MinT - Best Known (225−99, 225, s)-Nets in Base 4

Best Known (225−99, 225, s)-Nets in Base 4

(225−99, 225, 130)-Net over F₄ — Constructive and digital

Digital (126, 225, 130)-net over F₄, using

t-expansion [i] based on digital (105, 225, 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]

(225−99, 225, 239)-Net over F₄ — Digital

Digital (126, 225, 239)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−99, 225, 3561)-Net in Base 4 — Upper bound on s

There is no (126, 225, 3562)-net in base 4, because

1 times m-reduction [i] would yield (126, 224, 3562)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 735 245759 244498 812236 419996 418045 512270 615823 552241 448148 087246 480389 148340 152901 116778 987110 222209 266451 470148 967084 545471 423691 535860 > 4²²⁴ [i]