MinT - Best Known (226−99, 226, s)-Nets in Base 4

Best Known (226−99, 226, s)-Nets in Base 4

(226−99, 226, 130)-Net over F₄ — Constructive and digital

Digital (127, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 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]

(226−99, 226, 243)-Net over F₄ — Digital

Digital (127, 226, 243)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(226−99, 226, 3664)-Net in Base 4 — Upper bound on s

There is no (127, 226, 3665)-net in base 4, because

1 times m-reduction [i] would yield (127, 225, 3665)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2926 940971 328696 310648 519225 706532 640363 634277 201927 547182 150440 951219 388303 926136 700132 378846 579867 320965 304316 789824 249935 820239 275592 > 4²²⁵ [i]