MinT - Best Known (237−109, 237, s)-Nets in Base 4

Best Known (237−109, 237, s)-Nets in Base 4

(237−109, 237, 130)-Net over F₄ — Constructive and digital

Digital (128, 237, 130)-net over F₄, using

t-expansion [i] based on digital (105, 237, 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]

(237−109, 237, 217)-Net over F₄ — Digital

Digital (128, 237, 217)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−109, 237, 2945)-Net in Base 4 — Upper bound on s

There is no (128, 237, 2946)-net in base 4, because

1 times m-reduction [i] would yield (128, 236, 2946)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12286 398995 398648 634721 406311 196889 130524 856004 373904 047980 615770 688109 648514 634464 745914 310397 002570 128705 703261 950464 681415 975100 022963 940928 > 4²³⁶ [i]