MinT - Best Known (137, 137+117, s)-Nets in Base 4

Best Known (137, 137+117, s)-Nets in Base 4

(137, 137+117, 130)-Net over F₄ — Constructive and digital

Digital (137, 254, 130)-net over F₄, using

t-expansion [i] based on digital (105, 254, 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]

(137, 137+117, 230)-Net over F₄ — Digital

Digital (137, 254, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137, 137+117, 3117)-Net in Base 4 — Upper bound on s

There is no (137, 254, 3118)-net in base 4, because

1 times m-reduction [i] would yield (137, 253, 3118)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 212 807520 550956 865371 160110 228422 632885 338742 368228 025387 022219 821243 299618 907698 691747 226924 361340 114276 266308 009240 504175 436743 475517 481169 611214 691200 > 4²⁵³ [i]