MinT - Best Known (160−36, 160, s)-Nets in Base 4

Best Known (160−36, 160, s)-Nets in Base 4

(160−36, 160, 1044)-Net over F₄ — Constructive and digital

Digital (124, 160, 1044)-net over F₄, using

trace code for nets [i] based on digital (4, 40, 261)-net over F₂₅₆, using
- net from sequence [i] based on digital (4, 260)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(160−36, 160, 2638)-Net over F₄ — Digital

Digital (124, 160, 2638)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(160−36, 160, 565772)-Net in Base 4 — Upper bound on s

There is no (124, 160, 565773)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 136002 872422 478010 425496 962431 240547 411292 218457 838770 309687 659202 262317 558311 717358 390678 221120 > 4¹⁶⁰ [i]