MinT - Best Known (123, 123+115, s)-Nets in Base 4

Best Known (123, 123+115, s)-Nets in Base 4

(123, 123+115, 130)-Net over F₄ — Constructive and digital

Digital (123, 238, 130)-net over F₄, using

t-expansion [i] based on digital (105, 238, 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]

(123, 123+115, 187)-Net over F₄ — Digital

Digital (123, 238, 187)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+115, 2298)-Net in Base 4 — Upper bound on s

There is no (123, 238, 2299)-net in base 4, because

1 times m-reduction [i] would yield (123, 237, 2299)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49329 318850 124025 239305 773003 537164 963280 715980 397679 360693 048769 356076 867303 043289 185545 804270 087349 429606 670356 768255 574207 921417 024957 049550 > 4²³⁷ [i]