MinT - Best Known (129, 244, s)-Nets in Base 4

Best Known (129, 244, s)-Nets in Base 4

(129, 244, 130)-Net over F₄ — Constructive and digital

Digital (129, 244, 130)-net over F₄, using

t-expansion [i] based on digital (105, 244, 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]

(129, 244, 207)-Net over F₄ — Digital

Digital (129, 244, 207)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(129, 244, 2666)-Net in Base 4 — Upper bound on s

There is no (129, 244, 2667)-net in base 4, because

1 times m-reduction [i] would yield (129, 243, 2667)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 200 039694 388070 704166 953383 966542 425748 671168 246112 142052 254542 701485 840856 537776 218230 560764 741166 231667 348216 607055 136446 900469 053478 072572 617800 > 4²⁴³ [i]