MinT - Best Known (237−117, 237, s)-Nets in Base 4

Best Known (237−117, 237, s)-Nets in Base 4

(237−117, 237, 130)-Net over F₄ — Constructive and digital

Digital (120, 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]

(237−117, 237, 174)-Net over F₄ — Digital

Digital (120, 237, 174)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−117, 237, 2060)-Net in Base 4 — Upper bound on s

There is no (120, 237, 2061)-net in base 4, because

1 times m-reduction [i] would yield (120, 236, 2061)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12342 863334 559554 477547 621758 265587 122592 619819 336037 872258 372503 429297 537297 738896 926095 959022 081980 816246 324137 070549 405429 917814 946457 665280 > 4²³⁶ [i]