MinT - Best Known (225−103, 225, s)-Nets in Base 4

Best Known (225−103, 225, s)-Nets in Base 4

(225−103, 225, 130)-Net over F₄ — Constructive and digital

Digital (122, 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]

(225−103, 225, 210)-Net over F₄ — Digital

Digital (122, 225, 210)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−103, 225, 2876)-Net in Base 4 — Upper bound on s

There is no (122, 225, 2877)-net in base 4, because

1 times m-reduction [i] would yield (122, 224, 2877)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 737 456629 532432 748632 303219 257074 083065 250363 777213 497877 403777 313276 384618 956367 925407 447152 524819 948855 605776 477613 954177 709773 530292 > 4²²⁴ [i]