MinT - Best Known (126, 245, s)-Nets in Base 4

Best Known (126, 245, s)-Nets in Base 4

(126, 245, 130)-Net over F₄ — Constructive and digital

Digital (126, 245, 130)-net over F₄, using

t-expansion [i] based on digital (105, 245, 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]

(126, 245, 188)-Net over F₄ — Digital

Digital (126, 245, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 245, 2301)-Net in Base 4 — Upper bound on s

There is no (126, 245, 2302)-net in base 4, because

1 times m-reduction [i] would yield (126, 244, 2302)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 802 138158 781218 242630 966276 949106 177251 730538 977999 456571 927031 613786 734680 837180 307128 848860 613624 739170 829271 160561 068871 419479 184399 554467 529878 > 4²⁴⁴ [i]