MinT - Best Known (136, 136+117, s)-Nets in Base 4

Best Known (136, 136+117, s)-Nets in Base 4

(136, 136+117, 130)-Net over F₄ — Constructive and digital

Digital (136, 253, 130)-net over F₄, using

t-expansion [i] based on digital (105, 253, 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]

(136, 136+117, 227)-Net over F₄ — Digital

Digital (136, 253, 227)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 136+117, 3042)-Net in Base 4 — Upper bound on s

There is no (136, 253, 3043)-net in base 4, because

1 times m-reduction [i] would yield (136, 252, 3043)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 961171 718532 727389 646478 696703 565989 235244 300531 087751 227083 139485 947847 708600 601703 188787 365694 848999 152153 618651 467574 649826 381319 850827 733268 235800 > 4²⁵² [i]