MinT - Best Known (108, 108+79, s)-Nets in Base 4

Best Known (108, 108+79, s)-Nets in Base 4

(108, 108+79, 130)-Net over F₄ — Constructive and digital

Digital (108, 187, 130)-net over F₄, using

t-expansion [i] based on digital (105, 187, 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]

(108, 108+79, 231)-Net over F₄ — Digital

Digital (108, 187, 231)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(108, 108+79, 3784)-Net in Base 4 — Upper bound on s

There is no (108, 187, 3785)-net in base 4, because

1 times m-reduction [i] would yield (108, 186, 3785)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9657 253580 631912 685607 750113 575394 356852 252141 127383 486110 163018 175708 685100 797009 616947 955019 898770 975082 032720 > 4¹⁸⁶ [i]