MinT - Best Known (223−97, 223, s)-Nets in Base 4

Best Known (223−97, 223, s)-Nets in Base 4

(223−97, 223, 130)-Net over F₄ — Constructive and digital

Digital (126, 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]

(223−97, 223, 246)-Net over F₄ — Digital

Digital (126, 223, 246)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−97, 223, 3764)-Net in Base 4 — Upper bound on s

There is no (126, 223, 3765)-net in base 4, because

1 times m-reduction [i] would yield (126, 222, 3765)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 45 850090 656833 435046 911670 026101 105430 876270 695496 776618 655502 887325 859740 695838 314739 744623 172873 694103 111692 654198 628704 255822 086649 > 4²²² [i]