MinT - Best Known (239−121, 239, s)-Nets in Base 4

Best Known (239−121, 239, s)-Nets in Base 4

(239−121, 239, 130)-Net over F₄ — Constructive and digital

Digital (118, 239, 130)-net over F₄, using

t-expansion [i] based on digital (105, 239, 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]

(239−121, 239, 168)-Net over F₄ — Digital

Digital (118, 239, 168)-net over F₄, using

t-expansion [i] based on digital (115, 239, 168)-net over F₄, using
- net from sequence [i] based on digital (115, 167)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 115 and N(F) ≥ 168, using
    - Drinfeld modules of rank 1 [i]

(239−121, 239, 1840)-Net in Base 4 — Upper bound on s

There is no (118, 239, 1841)-net in base 4, because

1 times m-reduction [i] would yield (118, 238, 1841)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 197226 490508 465427 960549 148942 647227 889797 010870 947659 071251 790045 818024 850979 449244 723266 533117 476306 538996 584585 677953 282828 214435 477983 836480 > 4²³⁸ [i]